<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content="text/html; charset=iso-8859-1" = http-equiv=Content-Type> <META content="MSHTML 5.00.2614.3500" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV>Hi Bill,</DIV> <DIV> </DIV> <DIV>Thank you for your most enlightening post.</DIV> <DIV> </DIV> <DIV>Being a self taught tuner who is not a piano player (my theory on = the subject of tuning is lousy because I don't understand what a 6:3 octave = type is. I think its the 6th partial compared to the 3rd partial of the = higher note but am not sure)</DIV> <DIV> </DIV> <DIV>Anyway on the 1/21/2001 I answered a post from Richard Brekne which = is below.</DIV> <DIV> </DIV> <DIV>My comments</DIV> <DIV> </DIV> <DIV> "With me, this results (on a good piano) being maybe all = fifth's are a  1/4 beat per sec on the flat side and the fourth's are about 3/4 = beat per sec."<BR><BR>And</DIV> <DIV> </DIV> <DIV>"I would like to see a template written for a ETD that takes into consideration the         tuning of = octaves based on the octave and the octave and a fifth with the tuned note set at that = point equally between the two beats.  Does that make sense ?."</DIV> <DIV> </DIV> <DIV>I generally wind up by smoothing the lowest octave by 3 octaves and = a third for evenness.</DIV> <DIV> </DIV> <DIV>When you described your method you also confirmed to me that I am = correct in my method of tuning.  I have never been able to understand how = there can be several different stretches available on a ETD when in reality, on = any given piano, there is the natural sterch that we should be tuning for.</DIV> <DIV> </DIV> <DIV>As now at the age of 62, with hearing going, I am interested in a = ETD that is going to tune to what I want without having to set each note individually.  Thus my question, </DIV> <DIV> </DIV> <DIV>"I would like to see a template written for a ETD that takes into consideration the         tuning of = octaves based on the octave and the octave and a fifth with the tuned note set at that = point equally between the two beats.  Does that make sense ?."</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Tony Caught ICPTG<BR>Australia<BR><A href="mailto:caute@optusnet.com.au">caute@optusnet.com.au</A></DIV> <DIV><BR>Origonal sent 1/21/2001<BR><BR>snippety snip.<BR><BR>> That = being said.. I found it interesting to read his declaration = that<BR>matching<BR>> partials such that one has either a 2:1 or a 6:3 octave type, results in<BR>an<BR>> octave  with a "slight natural beat on the flat = side" and that tuning<BR>octaves<BR>> in which the natural beat is eliminated = when the unisons are tuned will be<BR>> "wider then the first seven of = Reyburn's so called octave stretches".<BR>These<BR>> followed by the statement = that "Jim Coleman's Pure 5ths temperament will<BR>result<BR>> in a natural = octave bead on the sharp side."<BR><BR>My 'learning' of tuning pianos is a little = different from many other more<BR>fortunate persons and I truely lack the ability = to express exactly what I<BR>mean cos I am dumb but, this natural beat is = the (to me) the sound or<BR>feeling you get when two notes blend in the = best.  I think I am trying to<BR>say 'when all audible harmonics are at their smoothest'.<BR><BR>With me, this results (on a good piano) being maybe = all fifth's are a  1/4<BR>beat per sec on the flat side and the = fourth's are about 3/4 beat per sec.<BR>><BR>> Notice that these statements = seem to apply equally to all ranges of the<BR>> piano... with no real = difference...ie a 6:3 octave in the high treble is<BR>still<BR>> going to yeild a = "narrow" natural beat octave.  Aside from that kind of<BR>> thing...these = statements open a door that might allow us to look closer = at<BR>the<BR>> possiblity that there is some phenomena going on that has been overlooked<BR>so<BR>> far by those from the ETD = world.<BR>><BR>> If its a hearable beat like thing we are looking for... and in the range<BR>Virgil<BR>> states... it should be measurable in some sense also.<BR>><BR>You will have noticed also that when tuning the bass in = same piano and you<BR>play a fifth, say C2, G2 whilst tuning C1 that you are = tuning to a beatless<BR>sound on octave and on octave fifth at the same time.<BR><BR>Next one is that after you tune a piano, check it and touch = up (one string<BR>at a time, others in note muted) the tuning with the sustain = pedal on. For<BR>some reason, possibley the interaction of all harmonics being = induced, a<BR>beat is audable which is the composite of all harmonic beats for = that note.<BR><BR>I would like to see a template written for a ETD that takes = into<BR>consideration the tuning of octaves based on the octave and the = octave and a<BR>fifth with the tuned note set at that point equally between the = two beats.<BR>Does that make sense ?.<BR><BR><BR>> --<BR>> Richard Brekne<BR>> RPT, N.P.T.F.<BR>> Bergen, Norway<BR>> <A href="mailto:Richard.Brekne@grieg.uib.no">mailto:Richard.Brekne@grieg.u= ib.no</A><BR>><BR>><BR>Regards<BR><BR>Tony Caught ICPTG<BR>Australia<BR><A href="mailto:caute@optusnet.com.au">caute@optusnet.com</A></DIV> <BLOCKQUOTE style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: = 0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A href="mailto:Billbrpt@AOL.COM" = title=Billbrpt@AOL.COM>Billbrpt@AOL.COM</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = href="mailto:pianotech@ptg.org" title=pianotech@ptg.org>pianotech@ptg.org</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, April 09, 2001 = 3:42 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Tempered Octaves = (was Beat Cancelers) </DIV> <DIV><BR></DIV><FONT face=arial,helvetica><FONT size=2>In a = message dated 4/7/01 9:34:40 PM Central Daylight Time, <BR><A href="mailto:ramsey@extremezone.com">ramsey@extremezone.com</A> = (Kevin E. Ramsey) writes: <BR><BR><BR> <BLOCKQUOTE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; = MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE">OK, Bill. You'll have to give a dummy like me a clue. Temperaments are one <BR>thing. Octave stretch is another. Jim Sr. = said that you had done <BR>"something" to your octaves, and that he liked it. = What did you do? I have <BR>found that the amount of stretch is a matter of = taste; what sounds pleasing <BR>to one tuner sounds noisy to another. So in = the interest of continuing <BR>education ( that holiest of grails which = we are always on a crusade for) <BR>clue me in. = Please?</BLOCKQUOTE><BR><BR>I came up with my octave tuning method back in the mid 1980's when I was = <BR>still tuning Equal Temperament (ET) but continued to use it when I started <BR>working with HT's.  I was strictly an aural tuner until after = the time I <BR>designed the Equal Beating Victorian Temperament (EBVT). =  The tuning Jim <BR>Coleman, Sr. RPT heard at the PTG Annual Convention in = 1993 was done entirely <BR>by ear.  Incidentally, he was sitting with = Virgil Smith RPT at the time who <BR>also came forward.  I remember Jim = turning to him noting that I had done the <BR>job aurally. <BR><BR>It is really very = simple but cuts right through to the very reason tempering <BR>is done in the = first place.  That is, the Pythagorean Comma, the "gap" <BR>between = what 7 pure octaves and 12 pure 5ths would create: about 24 cents.   <BR>It = uses the piano's natural inharmonicity to fill that gap and goes beyond = <BR>that to satisfy the ear's enigmatic desire to hear the upper registers = <BR>sharper than they should be theoretically. <BR><BR>Starting with a temperament = octave constructed with an appropriate amount of <BR>stretch (a compromise = between a 4:2 and a 6:3 octave or just a plain 6:3 <BR>octave for any of the = milder Well-Temperaments) ((the earlier HT's are more <BR>appropriately done = with a minimum amount of stretch)), begin stretching the <BR>octaves by = comparing the octave itself, moving closer to a pure 5th but being <BR>careful not = to make the resultant 4th sound too "busy". <BR><BR>Once you get into the 5th = octave, you will notice that the beating in the 4th <BR>ceases to be of = concern.  That is because the coincident partials are high <BR>enough that = they become so weak as to be inaudible.  As the 4ths become less <BR>significant, you can concentrate more on the compromise between = the octave <BR>and the 5th, trying to equalize the beating between them the best possible. <BR><BR>Now, once you have 2 full octaves, F3-F5, it becomes = very easy to determine <BR>the very best compromise for the octaves = possible.  Here is the method I use <BR>which I have never heard of anyone = else proposing at any time:  Using the <BR>Sostenuto pedal, play the = double octave, then the octave and a 5th.  Example, <BR>F3-F5, then = A#3(Bb3)-F5.  Find the point when the double octave sounds just <BR>barely = pure, then listen to the octave and 5th.  You should notice a <BR>pronounced = beat (which does not sound satisfying to the ear at all).  Now = <BR>sharpen the upper note, F5 until the double octave starts to beat and <BR>continue = sharpening until the double ocatve beats *exactly the same* as the = <BR>octave and 5th. <BR><BR>Both intervals will end up beating very slowly. =  In ET, they may well sound <BR>both to be *apparently* in tune, very nearly = beatless.  But, you can only <BR>find this "sweet spot" by comparing both intervals.  In a typical <BR>Well-Temperament, you will have some = pure 5ths and some tempered ones.  When <BR>the 5th is pure, the reconciliation of the double octave and the octave and <BR>5th will be = easy:  you can make both sound pure very easily.  When the 5ths = <BR>is tempered, you have to accept a little more beating in the double = octave <BR>than you would in ET. <BR><BR>So, you can see that when the tuning = concerns an Historical Temperament (HT) <BR>or any kind of = Well-Temperament (WT), using this method of determining <BR>octaves will create octaves = of *uneven* sizes just as the 3rds & 6ths (and <BR>other Rapidly = Beating Intervals) (RBI) are uneven in the temperament octave.   <BR>No = smooth curve calculation used by any Electronic Tuning Device (ETD) that I = <BR>know of can duplicate this although when tuning ET, they may closely <BR>approximate it. <BR><BR>The problem I see with using these smooth = curve calculations when tuning an <BR>HT is that they leave too much = dissatisfying tempering in the extensions of <BR>the 5ths, the octave and 5ths and = the double octave and 5ths.  This makes the <BR>resultant tuning have = less clarity than it could have otherwise.  For this <BR>reason, I = never use the FAC program with my Sanderson Accu-Tuner (SAT). <BR><BR>Back to = the method:  If the piano has no Sostenuto pedal, you can use the = <BR>damper pedal but use it the same way you would use the Sostenuto pedal. =  That <BR>is, play the notes in question first, then press the pedal to hold = them while <BR>you make your fine adjustment.  There will be a little = more background <BR>"noise" but you will still be able to clearly hear your = objective.  In a <BR>vertical piano using muting strips (as I do = and as I originally learned from <BR>Jim Coleman, Sr. RPT), the strip will be = under the dampers in the treble <BR>section.  You can just use the damper = pedal in the same manner as described <BR>above.   <BR><BR>Continue with = this method all the way to the top.  The piano's own <BR>inharmonicity = will determine where you tune each note.  When you have <BR>completed = the entire middle and treble sections, you can play double octaves <BR>and = octaves & 5ths up and down the scale.  Believe me, any octave and = 5ths <BR>which are too narrow will "jump out" at you.  I realized, = after a time that I <BR>could tune entirely by ear and have rock solid = consistency whether it was my <BR>first tuning of the day or the 6th or 7th for = that matter, whether I was <BR>tired, no matter what mood I was in or even = feeling somewhat ill because any <BR>notes that were too flat would be = glaringly apparent.  Notes which are too <BR>sharp will also produce = noticeable beating in the double octaves. <BR><BR>This method can be duplicated = exactly using the SAT (unfortunately, I don't <BR>know about the other ETD's). =  Having the SAT set on the note to be tuned, <BR>Example, F5: =  play the note F3 and stop the lights.  Now play the note <BR>A#3(Bb3). =  The lights will rotate clockwise.  Now press the Cents = button in <BR>the sharp direction until the lights slow down for A#3 and begin = to move <BR>counterclockwise for F3.  Find the point at which the = clockwise and <BR>counterclockwise movement is *equalized*. <BR><BR>At first, this = balance may be very close, especially if the piano has low <BR>inharmonicity = but it will be more pronounced as you move higher in the scale. <BR> In = ET, the difference between the two will probably be marginal.  In HT's, = <BR>the pure 5th and Double Octave combination will show stopped lights for = both <BR>the double octave and the octave and 5th while the tempered 5th = and double <BR>octave will show significant movement clockwise and = counterclockwise for both. <BR><BR>Once you have made your compromise for the note in = question, tune the note to <BR>whatever setting the SAT is showing.  If you = wish to store the tuning, do so <BR>before you move on to the next note. =  There is no reason why you couldn't use <BR>an FAC program that would get = you close to this compromise but which you <BR>could *customise* by making this = fine adjustment. <BR><BR>When tuning below the temperament octave and on to = the wound strings, you <BR>simply do a mirror image of what you did in the = treble.  Most people seem to <BR>want to tune the wound strings first. =  (I personally think using the FAC <BR>program starting at A0 is = *perverse*!).  I, however, have good reasons for <BR>finishing the top part of = the piano first.  It is by nature, the most <BR>difficult, tedious = and time consuming.  If you get the hard part done first, <BR>doing the = easy part last helps you relax and wind down as you complete the <BR>job. =  Also, if time is running out, you can move more quickly through the <BR>lowest = part of the piano than you can through the highest. <BR><BR>I usually will = complete the F3-F4 temperament octave, then tune down any <BR>notes in the low = tenor that may be below that first, then start moving <BR>upwards, leaving = the bass section for last.  For tuning the low tenor, <BR>compare the 4th, = 5th and octave. Make the octave sound just barely pure <BR>first, then listen = to the 4th and 5th.  In ET, the 5th will probably beat <BR>noticeably = and the 4th will be nearly pure.  Flatten the note to be tuned <BR>until = there is just a slight beat in the octave (around 1/2 beat per second) <BR>and = the 5th becomes cleaner and the 4th has a slow beat.  This should also <BR>produce a smooth progression of 3rds. <BR><BR>When tuning an HT, = you will have the same occurence with tempered 5ths and <BR>pure 5ths. =  The pure 5th compromise will be easy, the tempered a little more <BR>difficult. =  When tuning the so-called "poor scale design" piano (of which it = <BR>seems that most pianos are, in fact) you simply need to compare = all intervals <BR>and reach the best compromise.  The result will = probably be that your 3rds <BR>will beat more slowly than you anticipate and your = 5th may end up more <BR>tempered but the end effect on the music to be played = will be more pleasing.   <BR><BR>When tuning an HT with such a piano, you = really can end up with the sweet <BR>sounds prevailing over the harsh ones. =  In my view, the practice of *forcing* <BR>a more pure 5th in this area at = the expense of the octave, 4th and 3rd is a <BR>mistake.  It does not = make the piano sound better or cleaner.  It makes all <BR>of the = harmony sound more harshly than it has to. <BR><BR>When tuning the wound strings in = the bass section, do a mirror image of what <BR>you did in the treble. =  Example:  play the double octave F2-F4 and use the <BR>Sostenuto (or alternatively, the Damper) pedal to hold the notes open.   = <BR>Adjust the double octave until it sounds pure then listen to the octave and = <BR>5th, F2-C4.  Flatten F2 until the beat between the double octave and = the <BR>octave and 5th is *equalized*. <BR><BR>When using the SAT, set it = to the note to be tuned, Example: F2.  Play the <BR>note F4 and stop the = lights.  Now play the note C4 and the lights will rotate <BR>clockwise.  Press the Cents button in the Flat direction until the clockwise = <BR>and counterclockwise movement of the lights between C4 and F4 is *exactly* = <BR>the same.  Tune the note F2 to whatever setting is acheived.  If = you wish to <BR>store the tuning, do so before moving on to the next note. = <BR><BR>Playing double octaves and octave and 5ths up and down the = bass will reveal <BR>any unevenness, allowing you to acheive *maximum* clarity = and consistency.   <BR>If you have stored the tuning in the SAT, you = can check your work easily to <BR>make sure it has held as precisely as = you wish. <BR><BR>This method of equalizing beats between intervals is known as = none other than <BR>the Equal Beating (EB) method although I did not = realize this until I started <BR>to study the HT's.  It is also known as = "Meantone" tuning. So, don't let that <BR>word scare you away.  It does not necessarily involve the notorious "Wolf".   <BR>It simply means = making an equal compromise. <BR><BR>The important discovery in using the EB = principle in octaves as well as <BR>temperament is the Cancelling Out Effect (COE) = that has been brought to <BR>light.  It is well known that tuning the = piano with its 12 tone scale and <BR>Inharmonicity is a difficult puzzle to solve = which requires inevitable <BR>compromises.  You just can't really get = rid of some objectionable sounds, it <BR>seems.  But, if you will take = the hints I have given you here, you will see <BR>and hear that you really can = hide some of them and thus produce the sweetest, <BR>clearest sounding, most = melodic harmony possible from the piano, *regardless* <BR>of choice of = temperament. <BR><BR>Finally, to address the issue of *taste* in octave stretching: =  Yes, you will <BR>hear beating in single octaves, particularly = in the 6th and 7th octaves.   <BR>Some technicians get caught up in this = sound when played out of context.  But <BR>dwelling on an octave played = in the high treble by itself outside of a <BR>musical context is simply not = music, just as playing 3rds & 6ths up and down <BR>is not either. = <BR><BR>The decay in that part of the piano is quick.  The ear can tolerate = or even <BR>desire much more dissonance in an octave in that part of the piano = than it <BR>can in the middle.  Imagine a large, concert grand in a large = hall.  That <BR>dissonance in the upper octaves will actually help the = piano carry and <BR>project much better and thus provide a much more = satisfying sound than 2:1 <BR>octaves will. <BR><BR>Of course, there are = different circumstances.  Some customers, in the privacy <BR>and intimacy = of their homes will find that kind of stretch to be <BR>inappropriate. =  This may also be the case for chamber music or in a recording <BR>circumstance = where the piano is miked closely.  Any technician should be able <BR>to = modify his or her usual approach to suit the demands of the particular <BR>circumstances.  Indeed, tuning the way I have suggested in = the 7th octave <BR>will produce "errors" when tuning for the PTG RPT Tuning = Exam although it <BR>would probably not result in a failing score. =  When tuning for the Exam, the <BR>7th octave must be tuned in strict 2:1 = octaves in order to get a high or <BR>perfect score. <BR><BR>I hope this essay = enlightens many of you on the List. <BR><BR>Regards, <BR><BR>Bill Bremmer RPT <BR>Madison, Wisconsin</FONT> </FONT></BLOCKQUOTE></BODY></HTML>